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We determine the universal law for fidelity decayin quantum computations ofcomplex dynamics in presenceof internal static imperfections in a quantumcomputer. Our approach is based on random matrix theory applied toquantumcomputations in presence of imperfections.The theoretical predictions aretested and confirmed in extensive numerical simulations of a quantum algorithmfor quantum chaos in the dynamical tent map with up to 18 qubits. The theorydeveloped determines the time scales forreliable quantum computations inabsence of the quantum error correction codes. These time scales are related tothe Heisenberg time, the Thouless time, and the decay time given by Fermi'sgolden rule which are well known in the context of mesoscopic systems. Thecomparison is presented for static imperfection effects and random errors inquantum gates. A new convenientmethod for the quantum computation of thecoarse-grained Wigner function is also proposed

the european physical journal. d, atomic, molecular and optical physics/the european physical journal. d, atomic, molecular, optical and plasma physics

Quantum chaos and random matrix theory for fidelity decay in quantum computations with static imperfections